Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained i...Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.展开更多
Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research exten...Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.展开更多
This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt...This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.展开更多
This paper presents an approach that directly utilizes the Hessian matrix to investigate the existence and uniqueness of global solutions for the ECQP problem. The novel features of this proposed algorithm are its uni...This paper presents an approach that directly utilizes the Hessian matrix to investigate the existence and uniqueness of global solutions for the ECQP problem. The novel features of this proposed algorithm are its uniqueness and faster rate of convergence to the solution. The merit of this algorithm is base on cost, accuracy and number of operations.展开更多
By utilizing the time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements of signals received at a number of receivers, a constrained least-square （CLS） algorithm for estimating ...By utilizing the time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements of signals received at a number of receivers, a constrained least-square （CLS） algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of con- volute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time imple- mentation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square （WLS） approach especially for higher measurement noise level.展开更多
In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized...In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.展开更多
In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformul...In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global optimizations, which can be considered as an extension and a supplement of the previous results in canonical duality theory. Some examples are given to illustrate the applicability of our results.展开更多
A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, th...A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.展开更多
A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or...A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.展开更多
In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence...In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.展开更多
Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ...Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.展开更多
By adding one variable to the equality- or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimize...By adding one variable to the equality- or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.展开更多
The global solution for a coupled nonlinear Klein-Gordon system in two- dimensional space was studied. First, a sharp threshold of blowup and global existence for the system was obtained by constructing a type of cros...The global solution for a coupled nonlinear Klein-Gordon system in two- dimensional space was studied. First, a sharp threshold of blowup and global existence for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow. Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.展开更多
Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares sol...Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB = C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.展开更多
In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>...In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>1 and 3<α+β<6.We prove the existence of a ground state solution for the above problem in which the nonlinearity is not 4-superlinear at infinity.Also,using a discreetness property of Palais-Smale sequences and the Krasnoselkii genus method,we obtain the existence of infinitely many geometrically distinct solutions in the case whenα,β≥2 and 4≤α+β<6.展开更多
We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization ...We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.展开更多
In this paper, we present an effective meshless method for solving the inverse heat conduction problems, with the Neumann boundary condition. A PDE-constrained optimization method is developed to get a global approxim...In this paper, we present an effective meshless method for solving the inverse heat conduction problems, with the Neumann boundary condition. A PDE-constrained optimization method is developed to get a global approximation scheme in both spatial and temporal domains, by using the fundamental solution of the governing equation as the basis function.Since the initial measured data contain some noises, and the resulting systems of equations are usually ill-conditioned, the Tikhonov regularization technique with the generalized crossvalidation criterion is applied to obtain more stable numerical solutions. It is shown that the proposed schemes are effective by some numerical tests.展开更多
Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present...Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.展开更多
In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Ant...In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.展开更多
The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P^2 = I and s = ±1. By an eigenvalue decomposition of P, the constrained problem can be equiv...The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P^2 = I and s = ±1. By an eigenvalue decomposition of P, the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P. A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented. Moreover, a similar problem of the matrix equation with generalized constraint is discussed.展开更多
基金supported by the National Natural Science Foundation of China(62303095)the Natural Science Foundation of Sichuan Province(2023NSFSC0872).
文摘Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.
文摘Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.
基金This project is supported by the National Natural Science Foundation of China
文摘This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.
文摘This paper presents an approach that directly utilizes the Hessian matrix to investigate the existence and uniqueness of global solutions for the ECQP problem. The novel features of this proposed algorithm are its uniqueness and faster rate of convergence to the solution. The merit of this algorithm is base on cost, accuracy and number of operations.
基金supported by the National High Technology Research and Development Program of China (863 Program) (2010AA7010422 2011AA7014061)
文摘By utilizing the time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements of signals received at a number of receivers, a constrained least-square （CLS） algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of con- volute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time imple- mentation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square （WLS） approach especially for higher measurement noise level.
基金supported by the Natural Science Research Project of Department of Education of Guizhou Province(No.QJJ2023062)the National Natural Science Foundation of China(No.52174184)。
文摘In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.
文摘In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global optimizations, which can be considered as an extension and a supplement of the previous results in canonical duality theory. Some examples are given to illustrate the applicability of our results.
基金supported by the National Natural Science Foundation of China (60374063)the Natural Science Basic Research Plan Project in Shaanxi Province (2006A12)+1 种基金the Science and Technology Research Project of the Educational Department in Shaanxi Province (07JK180)the Emphasis Research Plan Project of Baoji University of Arts and Science (ZK0840)
文摘A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.
文摘A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.
文摘In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.
文摘Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.
基金supported by the National Natural Science Foundation of China (Nos. 10571116 and51075421)
文摘By adding one variable to the equality- or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.
基金Project supported by the National Natural Science Foundation of China (No.10271084)the Natural Science Foundation for Young Scholars of Sichuan Province of China (No.07JQ0094)
文摘The global solution for a coupled nonlinear Klein-Gordon system in two- dimensional space was studied. First, a sharp threshold of blowup and global existence for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow. Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
基金Supported by the Science Foundation Project of Tianshui Normal University(TSA1315)
文摘Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB = C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.
文摘In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>1 and 3<α+β<6.We prove the existence of a ground state solution for the above problem in which the nonlinearity is not 4-superlinear at infinity.Also,using a discreetness property of Palais-Smale sequences and the Krasnoselkii genus method,we obtain the existence of infinitely many geometrically distinct solutions in the case whenα,β≥2 and 4≤α+β<6.
文摘We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1129014311471066+3 种基金11572081)the Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)the Fundamental Research Funds for the Central Universities(Grant No.DUT15LK44)the Scientific Research Funds of Inner Mongolia University for the Nationalities(Grant No.NMD1304)
文摘In this paper, we present an effective meshless method for solving the inverse heat conduction problems, with the Neumann boundary condition. A PDE-constrained optimization method is developed to get a global approximation scheme in both spatial and temporal domains, by using the fundamental solution of the governing equation as the basis function.Since the initial measured data contain some noises, and the resulting systems of equations are usually ill-conditioned, the Tikhonov regularization technique with the generalized crossvalidation criterion is applied to obtain more stable numerical solutions. It is shown that the proposed schemes are effective by some numerical tests.
基金Subsidized by The Special Funds For Major State Basic Research Project G1999032803.
文摘Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.
文摘In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.
基金The work of the first author was supported by the Young Talent Foundation of Zhejiang Gongshang University
文摘The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P^2 = I and s = ±1. By an eigenvalue decomposition of P, the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P. A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented. Moreover, a similar problem of the matrix equation with generalized constraint is discussed.
